Wave-function inspired density functional applied to the H₂/H₂⁺ challenge

We start from the Bethe-Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional - BGE2 - which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair correlations. We demonstrate that BGE2 is size consistent and one-electron 'self-correlation' free. The electron-pair correlation coupling ensures the correct H₂ dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. BGE2 provides a good description of both H₂ and dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H₂ in a minimal basis. Our analysis shows that BGE2 captures essential features of the adiabatic connection path that current state-of-the-art DFT approximations do not.